Unless there's only something very simple wrong with it, like corrosion of a battery contact, there's no way to repair it. All the electronics is in a single hybrid module. Even when repair service was available from HP, repairs generally consisted of throwing away the hybrid module and installing a new one.

I'd like to get a non-functional HP-01 module (or a complete non-functional watch) for reverse-engineering. I want to take apart the module and photomicrograph the ROM chips to extract the bits for use in the Nonpareil simulator, as Peter Monta did with the HP-35. But obviously I'm not willing to do this to a working HP-01.

There is a U.S. patent on the HP-01 that includes some ROM source code, but it is definitely NOT the final release of the code as present in the actual product. The keyboard layout is slightly different, and the code in the patent is too large to fit in the two quads of ROM in an actual HP-01.